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Strong law of large numbers for fragmentation processes

S. C. Harris, R. Knobloch, A. E. Kyprianou (2010)

Annales de l'I.H.P. Probabilités et statistiques

In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1≥η>0.

Survival of homogeneous fragmentation processes with killing

Robert Knobloch, Andreas E. Kyprianou (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider a homogeneous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the decay of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.

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